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MaplePrimes Posts are for sharing your experiences, techniques and opinions about Maple, MapleSim and related products, as well as general interests in math and computing.

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  • The well known William Lowell Putnam Mathematical Competition (76th edition)  took place this month.
    Here is a Maple approach for two of the problems.

    1. For each real number x, 0 <= x < 1, let f(x) be the sum of  1/2^n  where n runs through all positive integers for which floor(n*x) is even.
    Find the infimum of  f.
    (Putnam 2015, A4 problem)

    local n, s:=0;
    for n to N do
      if type(floor(n*x),even) then s:=s+2^(-n) fi;
      #if floor(n*x) mod 2 = 0  then s:=s+2^(-n) fi;

    plot(f, 0..0.9999);


    min([seq(f(t), t=0.. 0.998,0.0001)]);



    So, the infimum is 4/7.
    Of course, this is not a rigorous solution, even if the result is correct. But it is a valuable hint.
    I am not sure if in the near future, a CAS will be able to provide acceptable solutions for such problems.

    2. If the function f  is three times differentiable and  has at least five distinct real zeros,
    then f + 6f' + 12f'' + 8f''' has at least two distinct real zeros.
    (Putnam 2015, B1 problem)

    F := f + 6*D(f) + 12*(D@@2)(f) + 8*(D@@3)(f);


    We are sugested to consider

    g3:=diff(g, x$3);


    So, F(x) = k(x) * g3 = k(x) * g'''
    g  has 5 distinct zeros implies g''' and hence F have 5-3=2 distinct zeros, q.e.d.


    A modified version of John May's modification of Bruce Char's animated Christmas tree, using some Maple 2015 features to automatically scale the 3D plot and automatically play the animation.

    I went with the viewpoint option, and removed the blinking lights. In the worksheet the tree shows as scaled larger. Perhaps it could be a submission to walkingrandomly.

    The CIELAB perceptual model of human vision can be used to predict the color of a wavelength in sRGB. I found the CIEDE2000 corrections to hue, chroma, and lighness were required to get the right values in the blue to violet region. The CIEDE2000 results seem pretty close to what I see looking through a diffraction grating considering I have no way of knowing how my eyes are adapted.

    Use the new, faster  version. It can run in under 1 minute;   and  WtoC_data.xlsx

    You will need the data for the color matching functions in the WtoC Excel File. The data directory can now be controlled in the mw file.


    This is a post that I wrote for the Altair Innovation Intelligence blog.

    I have a grudging respect for Victorian engineers. Isambard Kingdom Brunel, for example, designed bridges, steam ships and railway stations with nothing but intellectual flair, hand-calculations and painstakingly crafted schematics. His notebooks are digitally preserved, and make for fascinating reading for anyone with an interest in the history of engineering.

    His notebooks have several characteristics.

    • Equations are written in natural math notation
    • Text and diagrams are freely mixed with calculations
    • Calculation flow is clear and well-structured

    Hand calculations mix equations, text and diagrams.


    Engineers still use paper for quick calculations and analyses, but how would Brunel have calculated the shape of the Clifton Suspension Bridge or the dimensions of its chain links if he worked today?

    If computational support is needed, engineers often choose spreadsheets. They’re ubiquitous, and the barrier to entry is low. It’s just too easy to fire-up a spreadsheet and do a few simple design calculations.

     Spreadsheets are difficult to debug, validate and extend.


    Spreadsheets are great at manipulating tabular data. I use them for tracking expenses and budgeting.

    However, the very design of spreadsheets encourages the propagation of errors in equation-oriented engineering calculations

    • Results are difficult to validate because equations are hidden and written in programming notation
    • You’re often jumping about from one cell to another in a different part of the worksheet, with no clear visual roadmap to signpost the flow of a calculation

    For these limitations alone, I doubt if Brunel would have used a spreadsheet.

    Technology has now evolved to the point where an engineer can reproduce the design metaphor of Brunel’s paper notebooks in software – a freeform mix of calculations, text, drawings and equations in an electronic notebook. A number of these tools are available (including Maple, available via the APA website).

     Modern calculation tools reproduce the design metaphor of hand calculations.


    Additionally, these modern software tools can do math that is improbably difficult to do by hand (for example, FFTs, matrix computation and optimization) and connect to CAD packages.

    For example, Brunel could have designed the chain links on the Clifton Suspension Bridge, and updated the dimensions of a CAD diagram, while still maintaining the readability of hand calculations, all from the same electronic notebook.

    That seems like a smarter choice.

    Would I go back to the physical notebooks that Brunel diligently filled with hand calculations? Given the scrawl that I call my handwriting, probably not.

    I am learning to use maple for my notes preparation for the subject Finite Element Analysis. It is interesting to know that how often we blame maple or computer for the silly mistakes we made in our commands and expect the exact answers. I have used a small file and find it easy to analyse my mistakes fatser. If we make a small mistake in a big file, it not only gives us problem finding our mistakes, it leads to more mistakes in other parts as well. A command working in one document need not necessarily work the same way in other document.

    I have made my first document and people will come with suggestions to make appropriate modifications in the various sections to improve my knowledge on maple as well as the subject.


    Ramakrishnan V

    Most of the tags in this question example are rediculous "the, you, is, and, help, how," etc... .  I tried editing them but I cannot save tags to remove junk tags.  Above all, the most important tag to the question Poincare is not there.  This specific issue is for the recent question



    Since we’re almost at the end of the year, I thought it would be interesting to look back at our most popular webinars for academics in 2015. I found that they fell into one of two categories: live streaming webinars featuring Dr. Robert Lopez and Maple how-to tutorials.  (If you missed the live presentation, you can watch the recordings of all these webinars below.)

    The first and second most popular webinar were, unsurprisingly, both of the live streaming webinars that featured Dr. Robert Lopez (Emeritus Professor at Rose Hulman Institute of Technology and Maple Fellow at Maplesoft). These webinars were streamed live to an audience and allowed many people to get their first glimpse of the man behind the Clickable Calculus series and Teaching Concepts with Maple:

    1.       Eigenpairs Enlivened

    In this webinar, Dr. Robert Lopez demonstrates how Maple can enhance the task of teaching the eigenpair concept, and shows how Maple bridges the gap between the concept and the algorithms by which students are expected to practice finding eigenpairs.

    2.       Resequencing Concepts and Skills via Maple's Clickable

    In this webinar, Dr. Lopez presents examples of what "resequencing" looks like when implemented with Maple's point-and-click syntax-free paradigm. Not only can Maple be used to elucidate the concept, but in addition, it can be used to illustrate and implement the manipulations that ultimately the student must master.

    The next three were all brief webinars on how to complete specific tasks in Maple 2015. Just under a dozen of these were created in 2015 and they were all quite popular, but these three stood out above the rest:

    3.       Working with Data Sets in Maple

    This video walks through examples of working with several types of data in Maple, including visualizing stock and commodity data, forecasting future temperatures using weather data, and analyzing macroeconomic data, such as employment statistics, GDP and other economic indicators.

    4.       Custom Color Schemes in Maple

    This webinar provides an overview of the colorscheme option for coloring surfaces, curves and collections of points in Maple, including how to color with gradients, according to function value or point position. Examples of how the colorscheme option is used with various commands from the Maple library are also demonstrated.

     5.       Working with Units in Maple

    Maple 2015 allows for more fluid and natural interaction with units. This webinar provides an overview of the new unit formatting controls and new Temperature object, and demonstrates how to compute with units and tolerances.

    Are there any topics you’d like to see Robert cover in upcoming webinars? Or, any Maple how-to videos you think would be a helpful addition to our library? Let us know in the comments below!


    As some of you have previously mentioned, we have seen an increase in the amount of spam on MaplePrimes over the past few months. We recently took steps to improve it in a recent update that has so far proven helpful, and have also increased our behind-the-scenes efforts to proactively remove and block spam accounts.

    Today we made a couple of additional minor changes to member profiles that should help further. Specifically, members can no longer enter HTML tags in the biography, 'technical interests/fields', and 'other interests' sections within their profiles. Spammers were co-opting these areas to create links back to their sites, and it is our hope that MaplePrimes will become much less attractive to them now that the capability has been removed.

    In addition, we de-activated a large number of accounts (with 0 reputation) that were using these fields for spam. Prior to taking this action, we reviewed the records we were deactivating, and did not see any evidence of legitimate members. However, there is a small chance that we blocked a legitimate account in the process of doing this. If this has occurred to you, please accept my apologies and send an e-mail to and we will reactivate it quickly.


    I hope that in the future if mapleprimes ever does another overhaul that it does NOT do what has recently been done at the mathematica forum I just came across.

    Mapleprimes has endured a forum change from primes1 to primes2(current forum) and all posts/questions have for the most part remained intact, and have been repaired or fixed by the developers if pointed out .. thumbs up for Maplesoft and Mapleprimes developers for retaining all forum data.  Most posts that didn't have a home were simply relocated, but are still accessible.

    In the case for mathematica, a whole student forum was removed and is being scrutinized, and decided by mathematica developers whether or not the post should be put back into the forum (currently none of the posts have been restored).  I would think that would be most dissappointing from any user standpoint. 

    Um den Studierenden zu helfen, deren Mathematikkenntnisse nicht auf dem von Studienanfängern erwarteten Niveau waren, hat die TU Wien einen Auffrischungskurs mit Maple T.A. entwickelt.  Die vom Team der TU Wien ausgearbeiteten Fragen zu mathematischen Themen wie der Integralrechnung, linearen Funktionen, der Vektoranalysis, der Differentialrechnung und der Trigonometrie, sind in die Maple T.A. Cloud übernommen worden.  Außerdem haben wir diesen Inhalt als Kursmodul zur Verfügung gestellt.

    Laden Sie das Kursmodul der TU Wien herunter.

    Bei Interesse können Sie mehr über das Projekt der TU Wien in diesem Anwenderbericht lesen: Erfolgreiches Auffrischen von Mathematikkenntnissen an der Technischen Universität Wien mit Maple T.A.

    Maplesoft Product Manager, Maple T.A.

    Off to the right of mapleprimes we have Recent Questions/Maplesoft Blog Posts/Recent Posts and Active Conversations.

    I propose to have the category Workarounds added. 


    There are two instances I can think of that would be beneficial for Maple users that would belong here.  The most recent one and one regarding issues adding the dissipative term to the heat equations

    Users of older versions of Maple or even current Maple versions not yet updated would find this quite useful. 


    There are some great comments and replies by users that are worth upvoting.   Also choosing as best answer to some posts that were converted from questions would also be helpful here at mapleprimes.

    Here's a simple package for drawing knot diagrams and computing the Alexander polynomial. A typical usage case for the AlexanderPolynomial function is when a knot needs to be identified and only a visual representation of the knot is available. Then it's trivial to write down the Dowker sequence by hand and then the sequence can be used as an input for this package. The KnotDiagram function also takes the Dowker sequence as an input.


    TorusKnot(p, q) and PretzelKnot(p, q, r) are accepted as an input as well and can also be passed to the DowkerNotation function.


    The algorithm is fairly simple, it works as follows: represent each double point as a quadrilateral (two 'in' vertices and two 'out' vertices); connect the quads according to the Dowker specification; draw the result as a planar graph; erase the sides of each quad and draw its diagonals instead. This draws the intersections corresponding to the double points and guarantees that there are no other intersections. The knot polynomial is then computed from the diagram.


    The diagrams work fairly well for pretzel knots, but for certain knots they can be difficult to read because some of the quads around the double points can become too small or too skewed. Also, the code doesn't check that the generated quadrilaterals are convex (which is an implicit assumption in the algorithm).



    read "c:/math/prg/maple/knot.txt"




    [AlexanderPolynomial, DowkerNotation, KnotDiagram]


    AlexanderPolynomial([6, 8, 10, 2, 4], t)



    AlexanderPolynomial([4, 10, 14, 12, 2, 8, 6], t)



    AlexanderPolynomial([6, 18, 16, 14, -20, 4, 2, 22, 12, -8, -10], t)



    KnotDiagram([10, 12, -20, -16, -18, 2, 22, 24, -8, -4, -6, 14])


    AlexanderPolynomial([10, 12, -20, -16, -18, 2, 22, 24, -8, -4, -6, 14], t)



    AlexanderPolynomial([4, 8, 10, 16, 2, 18, 20, 22, 6, 14, 12], t)



    DowkerNotation(TorusKnot(5, 4))

    [-24, -10, 20, -30, -16, 26, -6, -22, 2, -12, -28, 8, -18, -4, 14]


    KnotDiagram(TorusKnot(5, 4))


    AlexanderPolynomial(TorusKnot(p, q), t); 1; simplify(subs([p = 5, q = 4], %))





    DowkerNotation(PretzelKnot(3, -4, 5))

    [-16, -14, 20, 22, 24, 18, -4, -2, 10, 12, 6, 8]


    KnotDiagram(PretzelKnot(3, -4, 5))


    AlexanderPolynomial(PretzelKnot(p, q, r), t)

    piecewise(p::odd and q::odd and r::odd, piecewise(p*q+p*r+q*r <> -1, (1/4)*signum(p*q+p*r+q*r+1)*((p*q+p*r+q*r)*(t^2-2*t+1)+t^2+2*t+1), 1), AlexanderPolynomial(PretzelKnot(p, q, r), t))


    eval(%, [p = 3, q = -4, r = 5])






    Mapleprimes should have an option to sort Mapleprimes by the date of the original poster.

    The Maple 2015.2 update is now available for Windows and Linux users. It provides official support for Windows 10, connectivity to the latest MATLAB release, support for MapleSim 2015.2, updates to Physics, and a variety of small improvements throughout the product.  It is available through the Check for Updates system, and is also available from our website on the Maple 2015.2 download page.

    The Mac update will be released as soon as we have finished fixing the problems on Mac OS X 10.11. We’re working on it.


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